Temperature Gradient Approximation Research Articles

Probing the Response of Tropical Deep Convection to Aerosol Perturbations Using Idealized Cloud-Resolving Simulations with Parameterized Large-Scale Dynamics

Abstract A framework is introduced to investigate the indirect effect of aerosol loading on tropical deep convection using three-dimensional limited-domain idealized cloud-system-resolving model simulations coupled with large-scale dynamics over fixed sea surface temperature. The large-scale circulation is parameterized using the spectral weak temperature gradient (WTG) approximation that utilizes the dominant balance between adiabatic cooling and diabatic heating in the tropics. The aerosol loading effect is examined by varying the number of cloud condensation nuclei (CCN) available to form cloud droplets in the two-moment bulk microphysics scheme over a wide range of environments from 30 to 5000 cm−3. The radiative heating is held at a constant prescribed rate in order to isolate the microphysical effects. Analyses are performed over the period after equilibrium is achieved between convection and the large-scale environment. Mean precipitation is found to decrease modestly and monotonically when the aerosol number concentration increases as convection gets weaker, despite the increase in cloud liquid water in the warm-rain region and ice crystals aloft. This reduction is traced down to the reduction in surface enthalpy fluxes as an energy source to the atmospheric column induced by the coupling of the large-scale motion, though the gross moist stability remains constant. Increasing CCN concentration leads to 1) a cooler free troposphere because of a reduction in the diabatic heating and 2) a warmer boundary layer because of suppressed evaporative cooling. This dipole temperature structure is associated with anomalously descending large-scale vertical motion above the boundary layer and ascending motion at lower levels. Sensitivity tests suggest that changes in convection and mean precipitation are unlikely to be caused by the impact of aerosols on cloud droplets and microphysical properties but rather by accounting for the feedback from convective adjustment with the large-scale dynamics. Furthermore, a simple scaling argument is derived based on the vertically integrated moist static energy budget, which enables estimation of changes in precipitation given known changes in surfaces enthalpy fluxes and the constant gross moist stability. The impact on cloud hydrometeors and microphysical properties is also examined, and it is consistent with the macrophysical picture.

Understanding the vertical structure of potential vorticity in tropical depressions

Potential vorticity (PV) has been used to understand the intensification and motion of a variety of tropical vortices. Here, atmospheric reanalyses and idealized models are used to understand how the vertical structures of moist convective heating and adiabatic advection jointly shape the vertical structures of PV in tropical depressions. Observationally based estimates reveal a top‐heavy PV structure in tropical depressions, contrasting with bottom‐heavy structures of absolute vorticity and diabatic PV generation. These distinct vertical structures are reproduced in an axisymmetric model which employs the weak temperature gradient approximation for conceptual simplicity and is forced by stratiform and deep convective heating. When applied in isolation, the stratiform and deep convective heatings produce PV maxima at 500 hPa and near the surface, respectively. When these two heatings are applied simultaneously, interactions between the stratiform and deep convective modes enhance the adiabatic advective tendencies produced by the transverse circulation, making the PV distribution more top‐heavy. In the lower and middle troposphere, radial advection also greatly reduces the radius of the PV structure relative to that of the imposed heating, consistent with structures in observed tropical depressions; the implications of these differences in radial structures for using the flux form of the relevant conservation equations (e.g. for PV substance or absolute vorticity) are discussed.

Inferences from Simple Models of Slow, Convectively Coupled Processes

Abstract A framework for conceptual understanding of slow, convectively coupled disturbances is developed and applied to several canonical tropical problems, including the water vapor content of an atmosphere in radiative–convective equilibrium, the relationship between convective precipitation and column water vapor, Walker-like circulations, self-aggregation of convection, and the Madden–Julian oscillation. The framework is a synthesis of previous work that developed four key approximations: boundary layer energy quasi equilibrium, conservation of free-tropospheric moist and dry static energies, and the weak temperature gradient approximation. It is demonstrated that essential features of slow, convectively coupled processes can be understood without reference to complex turbulent and microphysical processes, even though accounting for such complexity is essential to quantitatively accurate modeling. In particular, we demonstrate that the robust relationship between column water vapor and precipitation observed over tropical oceans does not necessarily imply direct sensitivity of convection to free-tropospheric moisture. We also show that to destabilize the radiative–convective equilibrium state, feedbacks between radiation and clouds and water vapor must be sufficiently strong relative to the gross moist stability.

The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

A diagnostic method is presented for analysing the large-scale behaviour of the Met Office Unified Model, which is a comprehensive atmospheric model used for weather and climate prediction. Outside the boundary layer, on scales larger than the radius of deformation, semi-geostrophic theory will give an accurate approximation to the model evolution. In particular, the ageostrophic circulation required to maintain geostrophic and hydrostatic balance against prescribed forcing and a rate of change of the geostrophic pressure can be calculated. In the tropics, the balance condition degenerates to the weak temperature gradient approximation. Within the boundary layer, the semi-geotriptic approximation has to be used because friction and rotation are equally important. Assuming the calculated pressure tendency and ageotriptic circulation match the observed model behaviour, the influence of the large-scale state and the nature of the forcing on the model response can be deduced in a straightforward way. The capabilities of the diagnostic are illustrated by comparing predictions of the ageotriptic circulation from the theory and the model. It is then used to show that the effects of latent heat release can be included by modifying the static stability, and to show the effect of an idealised tropical heat source on the subtropical jet. Finally, the response of the ageotriptic flow to boundary layer heating in the tropics is demonstrated. These illustrations show that the model behaviour on large scales conforms with theoretical expectations, so that the results of the diagnostic can be used to aid the development of further improvements to the model, in particular investigating systematic errors and understanding the large-scale atmospheric response to forcing.

A Linear Response Framework for Radiative‐Convective Instability

AbstractRadiative‐convective equilibrium is a simple paradigm for the tropical climate, in which radiative cooling balances convective heating in the absence of lateral energy transport. Recent studies have shown that a large‐scale circulation may spontaneously develop from radiative‐convective equilibrium through the interactions among water vapor, radiation, and convection. This potential instability, referred to as radiative‐convective instability, may be posed as a linear stability problem for the water vapor profile by combining a linear response framework with the weak temperature gradient approximation. We design two analytic models of convective linear response to moisture perturbations, which are similar to Betts‐Miller and bulk‐plume convection schemes. We combine these convective responses with either clear‐sky gray or real‐gas radiative responses. In all cases, despite consistent radiative feedbacks, the characteristics of convection dominate the vertical structure of the most unstable linear mode of water vapor perturbations. For Betts‐Miller convection, the stability critically depend on a key parameter: the heating to advection of moisture conversion rate (HAM); warmer atmospheres with higher HAM exhibit more linear instability. In contrast, bulk‐plume convection is stable across temperatures but becomes linearly unstable with a moisture mode peaking in the midtroposphere once combined to radiation, with approximate growth rates of 10 days.

The Implications of an Idealized Large-Scale Circulation for Mechanical Work Done by Tropical Convection

Abstract A thermodynamic analysis is presented of an overturning circulation simulated by two cloud-resolving models, coupled by a weak temperature gradient parameterization. Taken together, they represent two separated regions over different sea surface temperatures, and the coupling represents an idealized large-scale circulation such as the Walker circulation. It is demonstrated that a thermodynamic budget linking net heat input to the generation of mechanical energy can be partitioned into contributions from the large-scale interaction between the two regions, as represented by the weak temperature gradient approximation, and from convective motions in the active warm region and the suppressed cool region. Model results imply that such thermodynamic diagnostics for the aggregate system are barely affected by the strength of the coupling, even its introduction, or by the SST contrast between the regions. This indicates that the weak temperature gradient parameterization does not introduce anomalous thermodynamic behavior. We find that the vertical kinetic energy associated with the large-scale circulation is more than three orders of magnitude smaller than the typical vertical kinetic energy in each region. However, even with very weak coupling circulations, the contrast between the thermodynamic budget terms for the suppressed and active regions is strong and is relatively insensitive to the degree of the coupling. Additionally, scaling arguments are developed for the relative values of the terms in the mechanical energy budget.

Growth competition between columnar dendritic grains – Cellular automaton versus phase field modeling

Cellular Automaton (CA) simulations of two-dimensional growth competition among columnar dendritic grains are carried out for a succinonitrile - 0.4 wt% acetone alloy. This is achieved by computing the Grain Boundary (GB) orientation during directional solidification of a bi-crystal in a frozen temperature gradient approximation, each crystal being defined by its own orientation. Comparisons are subsequently conducted with recent Phase Field (PF) results derived under the same conditions as well as with the Geometrical Limit (GL) criterion and the Favorably Orientated Grain (FOG) criterion. The GL criterion is defined mathematically considering infinitely small branching within each grain in directions perpendicular to the main dendrite arms growth directions. The FOG criterion states survival of the grain having the growth direction best aligned with the temperature gradient. The GB orientation is investigated by CA simulations as a function of the cell size, the cell neighborhood and the position used to compute the growth velocity. Results reveal that sufficiently small cells lead to the convergence of the GB orientation towards the GL criterion, while sufficiently large cells lead to the FOG criterion. Within a range of intermediate cell size, excellent agreement is found with a revised version of the FOG criterion (rev-FOG) extracted from PF simulations over a wide range of grain orientations. The cell size needs to be of the order of the maximum step between primary stationary dendrite tips of the two competing grains. The Moore neighborhood provides better results than the von Neumann neighborhood. Noticeable improvement is also observed when computing the growth velocity at the leading dendrite tip positions compared to using the cell center approximation. With computational times several orders of magnitudes lower than PF, the CA method offers a realistic and useful alternative for direct simulations of solidification grain structures in casting processes. This work is also an example of upscaling between models, showing how PF dedicated to model phenomena at the scale of the solid-liquid interface and sidebranching competition can be used to evaluate and calibrate CA developed for large scale simulations.

Diurnal Cycle of the ITCZ in DYNAMO

Abstract During the 2011 special observing period of the Dynamics of the Madden–Julian Oscillation (DYNAMO) field experiment, two sounding arrays were established over the central Indian Ocean, one north and one south of the equator, referred to here as the NSA and SSA, respectively. Three-hourly soundings from these arrays augmented by observations of radiation and rainfall are used to investigate the diurnal cycle of ITCZ convection during the MJO suppressed phase. During the first half of October, when convection was suppressed over the NSA but prominent over the SSA, the circulation over the sounding arrays could be characterized as a local Hadley cell. Strong rising motion was present within the ITCZ extending across the SSA with compensating subsidence over the NSA. A prominent diurnal pulsing of this cell was observed, impacting conditions on both sides of the equator, with the cell running strongest in the early morning hours (0500–0800 LT) and notably weakening later in the day (1700–2000 LT). The declining daytime subsidence over the NSA may have assisted the moistening of the low to midtroposphere there during the pre-onset stage of the MJO. Apparent heating Q1 within the ITCZ exhibited a diurnal evolution from early morning bottom-heavy profiles to weaker daytime top-heavy profiles, indicating a progression from convective to stratiform precipitation. Making use of the weak temperature gradient approximation, results suggest that both horizontal radiative heating gradients and direct cloud radiative forcing have an important influence on diurnal variations of vertical motion and convection within the ITCZ.

Understanding Mesoscale Aggregation of Shallow Cumulus Convection Using Large‐Eddy Simulation

AbstractMarine shallow cumulus convection, often mixed with thin stratocumulus, is commonly aggregated into mesoscale patches. The mechanism and conditions supporting this aggregation are elucidated using 36 h large‐eddy simulations (LES) on a 128 × 128 km doubly periodic domain, using climatological summertime forcings for a location southeast of Hawaii. Within 12 h, mesoscale patches of higher humidity, more vigorous cumulus convection, and thin detrained cloud at the trade inversion base develop spontaneously. Mesoscale 16 × 16 km subdomains are composited into quartiles of column total water path and their heat and moisture budgets analyzed. The weak temperature gradient approximation is used to explain how apparent heating perturbations drive simulated mesoscale circulations, which in turn induce relative moistening of the moistest subdomains, a form of gross moist instability. Self‐aggregation is affected by precipitation and mesoscale feedbacks of radiative and surface fluxes but still occurs without them. In that minimal‐physics setting, the humidity budget analysis suggests self‐aggregation is more likely if horizontal‐mean humidity is a concave function of the horizontal‐mean virtual potential temperature, a condition favored by radiative cooling and cold advection within the boundary layer.

Diagnosing ENSO and Global Warming Tropical Precipitation Shifts Using Surface Relative Humidity and Temperature

AbstractLarge uncertainty remains in future projections of tropical precipitation change under global warming. A simplified method for diagnosing tropical precipitation change is tested here on present-day El Niño–Southern Oscillation (ENSO) precipitation shifts. This method, based on the weak temperature gradient approximation, assumes precipitation is associated with local surface relative humidity (RH) and surface air temperature (SAT), relative to the tropical mean. Observed and simulated changes in RH and SAT are subsequently used to diagnose changes in precipitation. Present-day ENSO precipitation shifts are successfully diagnosed using observations (correlationr= 0.69) and an ensemble of atmosphere-only (0.51 ≤r≤ 0.8) and coupled (0.5 ≤r≤ 0.87) climate model simulations. RH (r= 0.56) is much more influential than SAT (r= 0.27) in determining ENSO precipitation shifts for observations and climate model simulations over both land and ocean. Using intermodel differences, a significant relationship is demonstrated between method performance over ocean for present-day ENSO and projected global warming (r= 0.68). As a caveat, the authors note that mechanisms leading to ENSO-related precipitation changes are not a direct analog for global warming–related precipitation changes. The diagnosis method presented here demonstrates plausible mechanisms that relate changes in precipitation, RH, and SAT under different climate perturbations. Therefore, uncertainty in future tropical precipitation changes may be linked with uncertainty in future RH and SAT changes.

Idealized modeling of convective organization with changing sea surface temperatures using multiple equilibria in weak temperature gradient simulations

AbstractThe weak temperature gradient (WTG) approximation is a method of parameterizing the influences of the large scale on local convection in limited domain simulations. WTG simulations exhibit multiple equilibria in precipitation; depending on the initial moisture content, simulations can precipitate or remain dry for otherwise identical boundary conditions. We use a hypothesized analogy between multiple equilibria in precipitation in WTG simulations, and dry and moist regions of organized convection to study tropical convective organization. We find that the range of wind speeds that support multiple equilibria depends on sea surface temperature (SST). Compared to the present SST, low SSTs support a narrower range of multiple equilibria at higher wind speeds. In contrast, high SSTs exhibit a narrower range of multiple equilibria at low wind speeds. This suggests that at high SSTs, organized convection might occur with lower surface forcing. To characterize convection at different SSTs, we analyze the change in relationships between precipitation rate, atmospheric stability, moisture content, and the large‐scale transport of moist entropy and moisture with increasing SSTs. We find an increase in large‐scale export of moisture and moist entropy from dry simulations with increasing SST, which is consistent with a strengthening of the up‐gradient transport of moisture from dry regions to moist regions in organized convection. Furthermore, the changes in diagnostic relationships with SST are consistent with more intense convection in precipitating regions of organized convection for higher SSTs.

Land–Ocean Shifts in Tropical Precipitation Linked to Surface Temperature and Humidity Change

A compositing scheme that predicts changes in tropical precipitation under climate change from changes in near-surface relative humidity (RH) and temperature is presented. As shown by earlier work, regions of high tropical precipitation in general circulation models (GCMs) are associated with high near-surface RH and temperature. Under climate change, it is found that high precipitation continues to be associated with the highest surface RH and temperatures in most CMIP5 GCMs, meaning that it is the “rank” of a given GCM grid box with respect to others that determines how much precipitation falls rather than the absolute value of surface temperature or RH change, consistent with the weak temperature gradient approximation. Further, it is demonstrated that the majority of CMIP5 GCMs are close to a threshold near which reductions in land RH produce large reductions in the RH ranking of some land regions, causing reductions in precipitation over land, particularly South America, and compensating increases over ocean. Recent work on predicting future changes in specific humidity allows the prediction of the qualitative sense of precipitation change in some GCMs when land surface humidity changes are unknown. However, the magnitudes of predicted changes are too small. Further study, perhaps into the role of radiative and land–atmosphere feedbacks, is necessary.

Coupling with ocean mixed layer leads to intraseasonal variability in tropical deep convection: Evidence from cloud‐resolving simulations

AbstractThe effect of coupling a slab ocean mixed layer to atmospheric convection is examined in cloud‐resolving model (CRM) simulations in vertically sheared and unsheared environments without Coriolis force, with the large‐scale circulation parameterized using the Weak Temperature Gradient (WTG) approximation. Surface fluxes of heat and moisture as well as radiative fluxes are fully interactive, and the vertical profile of domain‐averaged horizontal wind is strongly relaxed toward specified profiles with vertical shear that varies from one simulation to the next. Vertical wind shear is found to play a critical role in the simulated behavior. There exists a threshold value of the shear strength above which the coupled system develops regular oscillations between deep convection and dry nonprecipitating states, similar to those found earlier in a much more idealized model which did not consider wind shear. The threshold value of the vertical shear found here varies with the depth of the ocean mixed layer. The time scale of the spontaneously generated oscillations also varies with mixed layer depth, from 10 days with a 1 m deep mixed layer to 50 days with a 10 m deep mixed layer. The results suggest the importance of the interplay between convection organized by vertical wind shear, radiative feedbacks, large‐scale dynamics, and ocean mixed layer heat storage in real intraseasonal oscillations.

Equilibrium response to carbon dioxide and aerosol forcing changes in a 1D air–sea interactive model

AbstractA 1D air–sea interactive model that couples an atmospheric column model with a slab ocean model was introduced. The model simulated an exact balance between radiative cooling and convective heating in the free troposphere. Within the planet boundary layer, the turbulent mixing produces cooling in the upper part and warming in the lower part, which is compensated by radiative and convective heating together. The model was then used to explore the equilibrium response of sea surface temperature (SST) and precipitation to carbon dioxide (CO2) and aerosol forcing changes. Results show a warming or cooling signal owning to increased CO2 or aerosols can be well captured by the ocean, leading to an increasing or decreasing of the SST, and hence the precipitation. Cutting off the interactions between atmosphere and ocean however renders different results. By applying the relaxed weak temperature gradient (WTG) approximation, the local response to aerosol forcing perturbations was investigated, which was shown to be largely different from the global response in spite of the same forcing. To understand the nonlinear interactions among different forcings, the equilibrium responses to multiple combinations of CO2 and aerosol forcings are analyzed.

The role of radiation in organizing convection in weak temperature gradient simulations

AbstractUsing a cloud system resolving model with the large scale parameterized by the weak temperature gradient approximation, we investigated the influence of interactive versus noninteractive radiation on the characteristics of convection and convective organization. The characteristics of convecting environments are insensitive to whether radiation is interactive compared to when it is not. This is not the case for nonconvecting environments; interactive radiative cooling profiles show strong cooling at the top of the boundary layer which induces a boundary layer circulation that ultimately exports moist entropy (or analogously moist static energy) from dry domains. This upgradient transport is associated with a negative gross moist stability, and it is analogous to boundary layer circulations in radiative convective equilibrium simulations of convective self‐aggregation. This only occurs when radiation cools interactively. Whether radiation is static or interactive also affects the existence of multiple equilibria‐steady states which either support precipitating convection or which remain completely dry depending on the initial moisture profile. Interactive radiation drastically increases the range of parameters which permit multiple equilibria compared to static radiation; this is consistent with the observation that self‐aggregation in radiative‐convective equilibrium simulations is more readily attained with interactive radiation. However, the existence of multiple equilibria in absence of interactive radiation suggests that other mechanisms may result in organization.

Modeling the Interaction between Quasigeostrophic Vertical Motion and Convection in a Single Column

Abstract A single-column modeling approach is proposed to study the interaction between convection and large-scale dynamics using the quasigeostrophic (QG) framework. This approach extends the notion of “parameterization of large-scale dynamics,” previously applied in the tropics via the weak temperature gradient approximation and other comparable methods, to the extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. The diabatic heating in an air column is resolved numerically by a single-column model or a cloud-resolving model. The large-scale vertical velocity, which controls vertical advection of temperature and moisture, is computed through the QG omega equation including the dry adiabatic terms and the diabatic heating term. The component due to diabatic heating can be thought of as geostrophic adjustment to that heating and couples the convection to the large-scale vertical motion. The approach is demonstrated using two representations of convection: a single-column model and linear response functions derived by Z. Kuang from a large set of cloud-resolving simulations. The results are qualitatively similar in both cases. The behavior of convection that is strongly coupled to large-scale dynamics is significantly different from that in the uncoupled case. The positive feedback of the diabatic heating on the large-scale vertical motion reduces the stability of the system, extends the decay time scale after initial perturbations, and increases the amplitude of convective responses to transient large-scale perturbations or imposed forcings. The diabatic feedback of convection on vertical motion is strongest for horizontal wavelengths on the order of the Rossby deformation radius.

Modeling the MJO in a cloud‐resolving model with parameterized large‐scale dynamics: Vertical structure, radiation, and horizontal advection of dry air

AbstractTwo Madden‐Julian Oscillation (MJO) events, observed during October and November 2011 in the equatorial Indian Ocean during the DYNAMO field campaign, are simulated in a limited‐area cloud‐resolving model using parameterized large‐scale dynamics. Three parameterizations of large‐scale dynamics—the conventional weak temperature gradient (WTG) approximation, vertical mode‐based spectral WTG (SWTG), and damped gravity wave coupling (DGW)—are employed. A number of changes to the implementation of the large‐scale parameterizations, as well as the model itself, are made and lead to improvements in the results. Simulations using all three methods, with imposed time‐dependent radiation and horizontal moisture advection, capture the time variations in precipitation associated with the two MJO events well. The three methods produce significant differences in the large‐scale vertical motion profile, however. WTG produces the most top‐heavy profile, while DGW's is less so, and SWTG produces a profile between the two, and in better agreement with observations. Numerical experiments without horizontal advection of moisture suggest that that process significantly reduces the precipitation and suppresses the top‐heaviness of large‐scale vertical motion during the MJO active phases. Experiments in which a temporally constant radiative heating profile is used indicate that radiative feedbacks significantly amplify the MJO. Experiments in which interactive radiation is used produce agreement with observations that is much better than that achieved in previous work, though not as good as that with imposed time‐varying radiative heating. Our results highlight the importance of both horizontal advection of moisture and radiative feedbacks to the dynamics of the MJO.

Response of Atmospheric Convection to Vertical Wind Shear: Cloud-System-Resolving Simulations with Parameterized Large-Scale Circulation. Part II: Effect of Interactive Radiation

Abstract The authors investigate the effects of cloud–radiation interaction and vertical wind shear on convective ensembles interacting with large-scale dynamics in cloud-resolving model simulations, with the large-scale circulation parameterized using the weak temperature gradient approximation. Numerical experiments with interactive radiation are conducted with imposed surface heat fluxes constant in space and time, an idealized lower boundary condition that prevents wind–evaporation feedback. Each simulation with interactive radiation is compared to a simulation in which the radiative heating profile is held constant in the horizontal and in time and is equal to the horizontal-mean profile from the interactive-radiation simulation with the same vertical shear profile and surface fluxes. Interactive radiation is found to reduce mean precipitation in all cases. The magnitude of the reduction is nearly independent of the vertical wind shear but increases with surface fluxes. Deep shear also reduces precipitation, though by approximately the same amount with or without interactive radiation. The reductions in precipitation due to either interactive radiation or deep shear are associated with strong large-scale ascent in the upper troposphere, which more strongly exports moist static energy and is quantified by a larger normalized gross moist stability.

The effect of large‐scale model time step and multiscale coupling frequency on cloud climatology, vertical structure, and rainfall extremes in a superparameterized GCM

AbstractThe effect of global climate model (GCM) time step—which also controls how frequently global and embedded cloud resolving scales are coupled—is examined in the Superparameterized Community Atmosphere Model ver 3.0. Systematic bias reductions of time‐mean shortwave cloud forcing (∼10 W/m2) and longwave cloud forcing (∼5 W/m2) occur as scale coupling frequency increases, but with systematically increasing rainfall variance and extremes throughout the tropics. An overarching change in the vertical structure of deep tropical convection, favoring more bottom‐heavy deep convection as a global model time step is reduced may help orchestrate these responses. The weak temperature gradient approximation is more faithfully satisfied when a high scale coupling frequency (a short global model time step) is used. These findings are distinct from the global model time step sensitivities of conventionally parameterized GCMs and have implications for understanding emergent behaviors of multiscale deep convective organization in superparameterized GCMs. The results may also be useful for helping to tune them.

Effect of Surface Fluxes versus Radiative Heating on Tropical Deep Convection

Abstract The effects of turbulent surface fluxes and radiative heating on tropical deep convection are compared in a series of idealized cloud-system-resolving simulations with parameterized large-scale dynamics. Two methods of parameterizing the large-scale dynamics are used: the weak temperature gradient (WTG) approximation and the damped gravity wave (DGW) method. Both surface fluxes and radiative heating are specified, with radiative heating taken as constant in the vertical in the troposphere. All simulations are run to statistical equilibrium. In the precipitating equilibria, which result from sufficiently moist initial conditions, an increment in surface fluxes produces more precipitation than an equal increment of column-integrated radiative heating. This is straightforwardly understood in terms of the column-integrated moist static energy budget with constant normalized gross moist stability. Under both large-scale parameterizations, the gross moist stability does in fact remain close to constant over a wide range of forcings, and the small variations that occur are similar for equal increments of surface flux and radiative heating. With completely dry initial conditions, the WTG simulations exhibit hysteresis, maintaining a dry state with no precipitation for a wide range of net energy inputs to the atmospheric column. The same boundary conditions and forcings admit a rainy state also (for moist initial conditions), and thus multiple equilibria exist under WTG. When the net forcing (surface fluxes minus radiative heating) is increased enough that simulations that begin dry eventually develop precipitation, the dry state persists longer after initialization when the surface fluxes are increased than when radiative heating is increased. The DGW method, however, shows no multiple equilibria in any of the simulations.